### Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

### Whole Numbers Only

Can you work out how many of each kind of pencil this student bought?

### The Patent Solution

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

# Double Digit

##### Stage: 3 Challenge Level:

To facilitate the ease of obtaining accurate results it would be useful to have calculators available for the children, particularly for the later extension ideas.

Children tackling this investigation will be:

• Using knowledge of place value
• Applying understanding of addition and division
• Choosing appropriate calculation strategies
• Working systematically to sort and organise data
• Recognising, explaining, generalising and predicting patterns
• Explaining methods of reasoning

It may be worth working through a few examples of the double-digit problem with the whole class so that the children get a feel for the procedure. Having done this, they are bound to start making their own predictions.

Before leaving them to investigate for themselves, it may be useful to talk about how they are going to record their results. This becomes particularly important when they come to tackle the three-digit extension suggested at the end. For those who reach this stage, a discussion about how to write down the six different triple-digit numbers systematically may prove valuable.

As usual, encourage children to talk to each other about their theories, helping them to express these clearly. Bring the class together as appropriate to share their findings and possible explanations.

The pupils themselves will come up with further variations to investigate so you can take on board their suggestions too.